#!/usr/bin/python
# -*- coding: utf-8 -*-
from __future__ import print_function
#! /usr/bin/env python
""" crypto.cipher.aes_sbox_analysis

    AES Sbox Analysis - a simple analysis of the AES Sbox that determines
    the number and size of the permutation subgroups in the transformation.
    Could be extended to examine any Sbox ...

    Copyright © (c) 2002 by Paul A. Lambert
    Read LICENSE.txt for license information.

    2002-12-05 Added validation of equation form of AES
    2002-06-01 Original
"""

# The AES Sbox
sbbytes = (0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5,
           0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
           0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0,
           0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
           0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc,
           0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
           0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
           0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
           0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0,
           0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
           0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b,
           0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
           0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85,
           0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
           0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5,
           0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
           0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17,
           0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
           0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88,
           0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
           0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c,
           0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
           0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9,
           0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
           0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6,
           0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
           0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e,
           0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
           0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94,
           0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
           0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68,
           0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16)


def groups(subbytes):
    gdict = {}     # a dictionary of the cycles indexed by the first cycle element
    touched = [0 for i in range(len(subbytes))]
    for i in range(len(sbbytes)):
        touched.append(0)
    for i in range(len(sbbytes)):
        element = i
        cycle = []
        if not touched[element]:
            for j in range(i, len(sbbytes)):
                touched[element] = 1
                cycle.append(element)
                element = sbbytes[element]
                if element == i:
                    break
            gdict[cycle[1]] = cycle
        else:
            pass
    return gdict


def grpv(subbytes):
    """" Returns a list of tuples (cycle start, cycle size) """
    v = []
    z = groups(subbytes)
    for i in z.keys():
        v.append([i, len(z[i])])
    return v


def sgv(subbytes):
    x = grpv(subbytes)
    sum = 0
    for i in x:
        sum = sum + i[1]
    return sum


def main():
    cycles = grpv(sbbytes)
    print('The AES sbox contains ',)
    print(len(cycles),)
    print('permutation subgroups')
    print('The AES sbox subgroups (start, length) are:')
    print(cycles)


# Make this test module runnable from the command prompt
if __name__ == "__main__":
    main()
